Context and Complementarity: Formalizing Bohr's Vision through Many-Valued Contextual Logic

TL;DR

This paper develops a formal, many-valued logical framework inspired by Bohr's complementarity and contextuality principles, to better model quantum paradoxes and potentially other context-dependent systems.

Contribution

It introduces a seven-valued, contextual logic based on Reichenbach's and Jain's logics, formalizing Bohr's ideas within a rigorous logical system.

Findings

Resolves quantum paradoxes without inconsistency or nonlocality.

Models incompatible measurements through conditional truths.

Extends applicability to psychology and cognitive science.

Abstract

Quantum mechanics challenges classical intuitions of space, time, and causality via the superposition principle, which allows systems to exist in multiple states simultaneously. Niels Bohr addressed these paradoxes through his Complementarity Principle, asserting that mutually exclusive properties-such as wave and particle behaviour-are jointly necessary for a complete description of quantum systems. Bohr also emphasized contextuality, the idea that measurement outcomes depend on the broader experimental setup. Despite his profound insights, Bohr did not offer a formal logical framework for these concepts. We address this gap by generalizing Reichenbach's three-valued logic into a seven-valued, formally contextual system, where contextuality is explicitly encoded via existential quantifiers. This logic retains Reichenbach's indeterminate value while modelling conditional truths across incompatible measurements, resolving key quantum paradoxes without logical inconsistency or nonlocality. Our approach draws inspiration from Jain logic which embraces multiple, context-dependent truths. Beyond quantum theory, this framework has potential applications in perceptual psychology and cognitive science, where context and contradiction also play central roles. The aim is to extend Bohr's legacy by equipping his epistemological vision with rigorous, many-valued logical tools.